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217 * 217 + 183 * 183

  • 70578
  • 82578
  • 80578
  • 80568

Answer: Option C

Explanation:

\begin{aligned}
\frac {1}{2}\times 2(a^2 + b^2) = \frac {1}{2} \times [(a + b)^2 + (a - b)^2]
\end{aligned}
\begin{aligned}
= \frac {1}{2} \times [(217 + 183)^2 + (217 - 183)^2] = 80578
\end{aligned}

Similar Questions :

1. How many terms are there in 2,4,8,16,....,1024

  • 7
  • 8
  • 9
  • 10

Answer: Option D

Explanation:

It is a GP. with r = 2, ie \begin{aligned} 2^1, 2^2, 2^3... \end{aligned}
If number of terms is n. Then,
\begin{aligned} 2 \times 2^{n-1} = 1024 \end{aligned} =>
\begin{aligned} 2^{n-1} = 512 \end{aligned}
or \begin{aligned} 2 \times 2^{n-1} = 2^9 \end{aligned}
so n-1 = 9 => n = 10

2. What least number must be subtracted from 427398 so that remaining number is divisible by 15

  • 3
  • 5
  • 7
  • 9

Answer: Option A

Explanation:

On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted

3. What is the largest 4 digit number exactly divisible by 88

  • 9900
  • 9999
  • 9988
  • 9944

Answer: Option D

Explanation:

Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944

4. Find the unit digit in \begin{aligned}
(544)^{102} + (544)^{103}
\end{aligned}

  • 2
  • 4
  • 0
  • 1

Answer: Option C

Explanation:

Required digit is = \begin{aligned}
(4)^{102} + (4)^{103} \end{aligned}
as \begin{aligned} (4)^2 \end{aligned} gives unit digit 6 so \begin{aligned} (4)^{102} \end{aligned} unit digit is 6 and \begin{aligned} (4)^{103} \end{aligned} unit digit is, unit digit of \begin{aligned} 6 \times 4 \end{aligned}= 4, so answer will be unit digit of 6 + 4 = 0

5. 7589 - X = 3434

  • 4155
  • 2321
  • 3155
  • None of above

Answer: Option A

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